{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# notes\n",
    "* Now I know I should think in column vector, and Tensorflow is very picky about the shape of data. But in numpy, the normal 1D ndarray is represented as column vector already. If I reshape $\\mathbb{R}^n$ as $\\mathbb{R}^{n\\times1}$, It's not the same as column vector anymore. It's Matrix with 1 column. And I got troubles with scipy optimizer. \n",
    "* So I should just treat tensorflow's data as special case. Keep using the convention of numpy world."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%reload_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "plt.style.use('fivethirtyeight')\n",
    "\n",
    "import sys\n",
    "sys.path.append('..')\n",
    "\n",
    "from helper import logistic_regression as lr  # my own module\n",
    "from helper import general as general\n",
    "\n",
    "from sklearn.metrics import classification_report"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>exam1</th>\n",
       "      <th>exam2</th>\n",
       "      <th>admitted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>34.623660</td>\n",
       "      <td>78.024693</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>30.286711</td>\n",
       "      <td>43.894998</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>35.847409</td>\n",
       "      <td>72.902198</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>60.182599</td>\n",
       "      <td>86.308552</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>79.032736</td>\n",
       "      <td>75.344376</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       exam1      exam2  admitted\n",
       "0  34.623660  78.024693         0\n",
       "1  30.286711  43.894998         0\n",
       "2  35.847409  72.902198         0\n",
       "3  60.182599  86.308552         1\n",
       "4  79.032736  75.344376         1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# prepare data\n",
    "data = pd.read_csv('ex2data1.txt', names=['exam1', 'exam2', 'admitted'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 3)\n",
      "(100,)\n"
     ]
    }
   ],
   "source": [
    "X = general.get_X(data)\n",
    "print(X.shape)\n",
    "\n",
    "y = general.get_y(data)\n",
    "print(y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# sigmoid function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x112c23278>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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IJAAA1HCmaWrGgr36btF+SVKAn7teGtVNzRpy8zqAykcgAQCgBjNNU1/8vEtz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112baffd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "ax.plot(np.arange(-10, 10, step=0.01),\n",
    "        lr.sigmoid(np.arange(-10, 10, step=0.01)))\n",
    "ax.set_ylim((-0.1,1.1))\n",
    "ax.set_xlabel('z', fontsize=18)\n",
    "ax.set_ylabel('g(z)', fontsize=18)\n",
    "ax.set_title('sigmoid function', fontsize=18)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# cost function\n",
    "> * $max(\\ell(\\theta)) = min(-\\ell(\\theta))$  \n",
    "> * choose $-\\ell(\\theta)$ as the cost function\n",
    "\n",
    "<img style=\"float: left;\" src=\"../img/logistic_cost.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = theta=np.zeros(3) # X(m*n) so theta is n*1\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.69314718055994529"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.cost(theta, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "looking good, be careful of the data shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# gradient\n",
    "* this is batch gradient  \n",
    "* translate this into vector computation $\\frac{1}{m} X^T( Sigmoid(X\\theta) - y )$\n",
    "\n",
    "<img style=\"float: left;\" src=\"../img/logistic_gradient.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -0.1       , -12.00921659, -11.26284221])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.gradient(theta, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# fit the parameter\n",
    "> * here I'm using [`scipy.optimize.minimize`](http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html#scipy.optimize.minimize) to find the parameters  \n",
    "> * and I use this model without understanding.... what is `Jacobian` ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy.optimize as opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "res = opt.minimize(fun=lr.cost, x0=theta, args=(X, y), method='Newton-CG', jac=lr.gradient)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     fun: 0.20349771447597362\n",
      "     jac: array([  9.71219458e-06,   6.96602898e-04,   8.53722702e-04])\n",
      " message: 'Optimization terminated successfully.'\n",
      "    nfev: 73\n",
      "    nhev: 0\n",
      "     nit: 29\n",
      "    njev: 253\n",
      "  status: 0\n",
      " success: True\n",
      "       x: array([-25.17064404,   0.20630619,   0.20154693])\n"
     ]
    }
   ],
   "source": [
    "print(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# predict and validate from training set\n",
    "> now we are using training set to evaluate the model, this is not the best practice, but the course just begin, I guess Andrew will cover how to do model validation properlly later"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             precision    recall  f1-score   support\n",
      "\n",
      "          0       0.87      0.85      0.86        40\n",
      "          1       0.90      0.92      0.91        60\n",
      "\n",
      "avg / total       0.89      0.89      0.89       100\n",
      "\n"
     ]
    }
   ],
   "source": [
    "final_theta = res.x\n",
    "y_pred = lr.predict(X, final_theta)\n",
    "\n",
    "print(classification_report(y, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# find the decision boundary\n",
    "http://stats.stackexchange.com/questions/93569/why-is-logistic-regression-a-linear-classifier\n",
    "> $X \\times \\theta = 0$  (this is the line)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-25.17064404   0.20630619   0.20154693]\n"
     ]
    }
   ],
   "source": [
    "print(res.x) # this is final theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 124.88725955   -1.02361365   -1.        ]\n"
     ]
    }
   ],
   "source": [
    "coef = -(res.x / res.x[2])  # find the equation\n",
    "print(coef)\n",
    "\n",
    "x = np.arange(130, step=0.1)\n",
    "y = coef[0] + coef[1]*x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>exam1</th>\n",
       "      <th>exam2</th>\n",
       "      <th>admitted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>65.644274</td>\n",
       "      <td>66.221998</td>\n",
       "      <td>0.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>19.458222</td>\n",
       "      <td>18.582783</td>\n",
       "      <td>0.492366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>30.058822</td>\n",
       "      <td>30.603263</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>50.919511</td>\n",
       "      <td>48.179205</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>67.032988</td>\n",
       "      <td>67.682381</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>80.212529</td>\n",
       "      <td>79.360605</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>99.827858</td>\n",
       "      <td>98.869436</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            exam1       exam2    admitted\n",
       "count  100.000000  100.000000  100.000000\n",
       "mean    65.644274   66.221998    0.600000\n",
       "std     19.458222   18.582783    0.492366\n",
       "min     30.058822   30.603263    0.000000\n",
       "25%     50.919511   48.179205    0.000000\n",
       "50%     67.032988   67.682381    1.000000\n",
       "75%     80.212529   79.360605    1.000000\n",
       "max     99.827858   98.869436    1.000000"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()  # find the range of x and y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> you know the intercept would be around 125 for both x and y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1150bbb70>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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NxpdffllmXlypdevWsXPnTjZu3EiLFi0c1mW1Wnn44YeJiIhg3bp15e43b97cvpr6WvMP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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112c648d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set(context=\"notebook\", style=\"ticks\", font_scale=1.5)\n",
    "\n",
    "sns.lmplot('exam1', 'exam2', hue='admitted', data=data, \n",
    "           size=6, \n",
    "           fit_reg=False, \n",
    "           scatter_kws={\"s\": 25}\n",
    "          )\n",
    "\n",
    "plt.plot(x, y, 'grey')\n",
    "plt.xlim(0, 130)\n",
    "plt.ylim(0, 130)\n",
    "plt.title('Decision Boundary')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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